Non-convex compressed sensing with frequency mask for seismic data reconstruction and denoising

Compressed Sensing has recently proved itself as a successful tool to help address the challenges of acquisition and processing seismic data sets. Compressed sensing shows that the information contained in sparse signals can be recovered accurately from a small number of linear measurements using a sparsity-promoting regularization. This paper investigates two aspects of compressed sensing in seismic exploration: (i) using a general non-convex regularizer instead of the conventional one-norm minimization for sparsity promotion and (ii) using a frequency mask to additionally subsample the acquired traces in the frequency-space (f-x) domain. The proposed non-convex regularizer has better sparse recovery performance compared with one-norm minimization and the additional frequency mask allows us to incorporate a priori information about the events contained in the wavefields into the reconstruction. For example, (i) seismic data are band-limited; therefore one can use only a partial set of frequency coefficients in the range of reflections band, where the signal-to-noise ratio is high and spatial aliasing is low, to reconstruct the original wavefield, and (ii) low-frequency characteristics of the coherent ground rolls allow direct elimination of them during reconstruction by disregarding the corresponding frequency coefficients (usually bellow 10 Hz) via a frequency mask. The results of this paper show that some challenges of reconstruction and denoising in seismic exploration can be addressed under a unified formulation. It is illustrated numerically that the compressed sensing performance for seismic data interpolation is improved significantly when an additional coherent subsampling is performed in the f-x domain compared with the t-x domain case. Numerical experiments from both simulated and real field data are included to illustrate the effectiveness of the presented method.